Here's a really quick way to check things between Duelist and Great Weapon Fighting. I know D&D is not balanced against PVP, but lets just try something. A comparison between a sword and board fighter and a great weapon fighter with and without their styles, against each other. Yes, the dreaded DPR. Well, DPA (damage per attack).
Level 1-3, chain mail, Str 16
Sword and Board
AC 18, Attack +5, Damage 1d8+3 (7.5); vs AC 16, 50% chance to hit: (7.5*0.5)+(4.5*0.05crit)=3.975
Greatsword
AC 16, Attack +5, Damage 2d6+3 (10); vs AC 18, 40% chance to hit: (10*0.4)+(7*0.05crit)=4.35; greatsword is ahead by 9%, which I think is within tolerance.
What about styles? Level 1-3
Duelist
AC 18, Attack +5, Damage 1d8+5 (9.5); vs AC 16, 50% chance to hit: (9.5*0.5)+(4.5*0.05crit)=4.975
Greatsword
AC 16, Attack +5, Damage 2d6*+3 (11.33...); vs AC 18, 40% chance to hit: (11.33..*0.4)+(8.33...*0.05crit)=4.95; longsword is ahead by a negligible amount.
Lets jump up to higher levels
Level 8; Str 20, Plate armor
Sword and Board (no style)
AC 20, Attack +8, Damage 1d8+5 (9.5); vs AC 18 is 55% to hit: (9.5*0.55)+(4.5*0.05crit)=5.45
Greatsword (no style)
AC 18, Attack +8, Damage 2d6+5 (12); vs AC 18 is 45% to hit: (12*0.45)+(7*0.05crit)=5.75; greatsword is ahead by 6%
Greataxe (no style)
AC 18, Attack +8, Damage 1d12+5 (11.5); vs AC 18 is 45% to hit: (11.5*0.45)+(6.5*0.05crit)=5.5; greataxe is ahead by 1%.
Now for styles:
Duelist
AC 20, Attack +8, Damage 1d8+7 (11.5); vs AC 18 is 55% to hit: (11.5*0.55)+(4.5*0.05crit)=6.5775
Great Weapon Fighter
AC 18, Attack +8, Damage 2d6*+5 (13.33...); vs AC 18 is 45% to hit: (13.33...*0.45)+(8.33...*0.05crit)=6.4167; longsword is like 3% ahead, so it's gained a little more.
And just for comparison; great axe great weapon fighter:
AC 18, Attack +8, Damage 1d12*+5 (12.33...); vs AC 18 is 45% to hit: (12.33...*0.45)+(7.33...*0.05crit)=5.9167; longsword is 11% ahead ...
So, the argument that Duelist is better than GWFing because great weapons start out better than one-handed weapons MIGHT be true. But, adding the greataxe into the mix makes me wonder if the 2d6 combined with great weapon fighting is causing the problem. If great weapon fighting was better, and great weapons were 1d12 instead of 2d6, then they may be better off.
But, since the two characters are likely fighting against the same AC, not each other, a great weapon wielder does have a higher likelyhood of killing the creature before it can get an extra attack, negating a whole attack that the shield AC would have negated. Shields mean 10% of attacks are going to miss, so a fight would have to go 10 rounds before that shield added up to that extra attack avoided. Fights go faster than that, so a great weapon may still be the better choice.